# Square Roots - How to Simplify Square Roots - Part 1

## How to Simplify Square Roots with Prime Numbers- How it Works - Video

### Example 1

Example 1:

When simplifying square roots or radicals, we need to look for square numbers, since squares are the inverse of square roots. We need to rewrite 20 as a factor pair where one number is a prime number. We have the options to rewrite 20 as 1*20 or 2*10 or 4*5. Since we want prime numbers, we can choose 2*10 or 4*5. Both will give you the same answer, and in this case we will work with 2*10.

√20

• √(2 * 10) We rewrite as a multiplication of two numbers.

• (2*2*5) We rewrite 10 as a multiplication of two numbers.

• 22 * 5 We rewrite 2 * 2 as 22.

• 2 * √5 We cancel the inverses of square and square root.

• 2√5 We drop the multiplication symbol.

So 2√5 is the final answer.

### Example 2

Example 2:

When simplifying square roots or radicals, we need to look for square numbers, since squares are the inverse of square roots. We need to rewrite 105 as a factor pair where one number is a prime number. We have the options to rewrite 105 as 1*105 or 3*35 or 5*21. Since we want prime numbers, we can choose 3*35 or 5*21. Both will give you the same answer, and in this case we will work with 3*35.

-105

• -√(3 * 35) We rewrite as a multiplication of two numbers.

• -√(3*5*7) We rewrite 35 as a multiplication of two numbers.

• -105 We multiply the numbers because we don't have two of the same number.

So -√105 is the final answer.

### Example 3

Example 3:

When simplifying square roots or radicals, we need to look for square numbers, since squares are the inverse of square roots. We need to rewrite 72 as a factor pair where one number is a prime number. We have the options to rewrite 72 as 1*72 or 2*36 or 3*24. Since we want prime numbers, we can choose 2*36 or 3*24. Both will give you the same answer, and in this case we will work with 2*36.

72

• √(2 * 36) We rewrite as a multiplication of two numbers.

• √(2 * 2 * 18) We rewrite 36 as a multiplication of two numbers.

• √(2 * 2 * 2 * 9) We rewrite 18 as a multiplication of two numbers.

• √(2 * 2 * 2 * 3 * 3) We rewrite 9 as a multiplication of two numbers.

• √(22 * 32 * 2) We rewrite 2 * 2 as 22 and 3 * 3 as 32.

• 2 * 3 * √2 We cancel the inverses of square and square root.

• 6*2 We multiply the numbers in front of the square root.

• 6√2 We drop the multiplication symbol.

So 62 is the final answer.

### Example 4

Example 4:

When simplifying square roots or radicals, we need to look for square numbers, since squares are the inverse of square roots. We need to rewrite 41 as a factor pair where one number is a prime number. We only the option to rewrite 41 as 1*41. None of those factor pairs are greater than one so we can't simplify anymore.

-41

• -1 * 41 We rewrite as a multiplication of two numbers.

• -√41 We can't simplify any further.

So -√41 is the final answer.

## Live Worksheet

Here is the link if you prefer.